Unless you have some way of proving that one-way functions exist, which would imply as a consequence P ≠ NP, this is literally untrue (unless by "eventually" you mean "one day centuries hence, maybe we'll prove P ≠ NP"). There is not a single piece of crypto that can be proven correct today; all crypto that we use is safe because mathematicians have so far been unable to find a practical way to break.
This requires mathematicians to be actively trying to break the crypto, so personalities matter because you can't get a worldwide community of experts to study every random person's algorithm. This also requires mathematicians to have a sense of which ways a particular algorithm might be fragile, even if they can't break it quite yet, which requires some non-mathematically-provable trust in the cryptanalyst's good sense.
And, of course, if you believe that a certain cryptographer might be inserting back doors or prone to approving crypto that has back doors (see for instance Dual_EC_DRBG), you might distrust other output from that same cryptographer even if you can't prove anything yet.